Finite Group Databasebeta

← C5×#9390 #11932110

Subgroups — C5×#9390 #11932110

Order 1280.

446 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2921C211yesmaximal, characteristic
2C5×#2611C211yesmaximal, characteristic
3C5×#1528C212yesmaximal, complemented
4C5×#1464C211yesmaximal, characteristic
5C5×#1300C212yesmaximal, complemented
6C2×C5×#125C2211yescharacteristic
7C2×C5×#117C2211yescharacteristic
8C5×#433—24no—
9C5×#432C2212yes—
10C5×#423—21no—
11C5×#407—21no—
12C4×C5×M16C2212yes—
13C5×#400C411yescharacteristic
14C5×#399C411yescharacteristic
15C5×#398C411yescharacteristic
16C5×#397C411yescharacteristic
17C5×#389—21no—
18C5×#388—21no—
19C5×#387—21no—
20C5×#385—21no—
21C5×#376C2211yescharacteristic
22C5×#330—24no—
23C5×#324—21no—
24C5×#323—21no—
25#9390C511yesmaximal, characteristic, direct product factor, Sylow
26C23×C4×C5D411yescharacteristic
27C2×C5×M16—22no—
28C5×#125—22no—
29C5×#125—22no—
30C5×#117—22no—
31C5×#117—22no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4C2×C411yescharacteristic
37C2×C5×C4⋊C4C2×C411yescharacteristic
38C2×C5×C4⋊C4C2×C411yescharacteristic
39C2×C5×C4⋊C4D411yescharacteristic
40C2×C5×C22⋊C4—21no—
41C2×C5×C22⋊C4—21no—
42C2×C5×C22⋊C4C2×C411yescharacteristic
43C2×C5×C22⋊C4D411yescharacteristic
44C2×C42×C5—21no—
45C2×C42×C5D411yescharacteristic
46C2×C42×C5C2311yescharacteristic
47C5×C4⋊C8—24no—
48C5×C4⋊C8—22no—
49C5×C22⋊C8—24no—
50C5×C22⋊C8—22no—
51C5×#97—22no—
52C5×#97D414yes—
53C4×C5×C8—22no—
54C5×#95—21no—
55C5×#95—21no—
56C5×#95—21no—
57C5×#95—21no—
58C5×#95—21no—
59C5×#95C2×C411yescharacteristic
60C5×#95C2×C411yescharacteristic
61#2921C2×C511yescharacteristic
62#2611C2×C511yescharacteristic
63#1528C2×C512yescomplemented
64#1464C2×C511yescharacteristic
65#1300C2×C512yescomplemented
66C24×C5C22⋊C411yescharacteristic
67C22×C4×C5—21no—
68C22×C4×C5—21no—
69C22×C4×C5—21no—
70C22×C4×C5—21no—
71C22×C4×C5—21no—
72C22×C4×C5—21no—
73C22×C4×C5—41no—
74C22×C4×C5—41no—
75C22×C4×C5C22⋊C411yescharacteristic
76C22×C4×C5C22⋊C411yescharacteristic
77C22×C4×C5C22⋊C411yescharacteristic
78C22×C4×C5C22×C411yescharacteristic
79C22×C4×C5C2×D411yescharacteristic
80C22×C4×C5C2×D411yescharacteristic
81C5×M16—42no—
82C5×M16—42no—
83C2×C5×C8—24no—
84C2×C5×C8—42no—
85C5×C4⋊C4—22no—
86C5×C4⋊C4—22no—
87C5×C4⋊C4—22no—
88C5×C4⋊C4—22no—
89C5×C4⋊C4—42no—
90C5×C4⋊C4—42no—
91C5×C4⋊C4—41no—
92C5×C4⋊C4—42no—
93C5×C4⋊C4—41no—
94C5×C22⋊C4—22no—
95C5×C22⋊C4—22no—
96C5×C22⋊C4—42no—
97C5×C22⋊C4—42no—
98C42×C5—21no—
99C42×C5—21no—
100C42×C5—42no—
101C42×C5C2×D412yes—
102C42×C5#4112yes—
103C2×#125C22×C511yescharacteristic
104C2×#117C22×C511yescharacteristic
105#433—24no—
106#432C22×C512yes—
107#423—21no—
108#407—21no—
109C4×M16C22×C512yes—
110#400C4×C511yescharacteristic
111#399C4×C511yescharacteristic
112#398C4×C511yescharacteristic
113#397C4×C511yescharacteristic
114#389—21no—
115#388—21no—
116#387—21no—
117#385—21no—
118#376C22×C511yescharacteristic
119#330—24no—
120#324—21no—
121#323—21no—
122C23×C5—21no—
123C23×C5—21no—
124C23×C5—21no—
125C23×C5—41no—
126C23×C5—41no—
127C23×C5C2×C22⋊C411yescharacteristic
128C2×C4×C5—21no—
129C2×C4×C5—21no—
130C2×C4×C5—22no—
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5—21no—
135C2×C4×C5—21no—
136C2×C4×C5—41no—
137C2×C4×C5—41no—
138C2×C4×C5—42no—
139C2×C4×C5—42no—
140C2×C4×C5—41no—
141C2×C4×C5—41no—
142C2×C4×C5—41no—
143C2×C4×C5—41no—
144C2×C4×C5—41no—
145C2×C4×C5—41no—
146C2×C4×C5—41no—
147C2×C4×C5—41no—
148C2×C4×C5—41no—
149C2×C4×C5—41no—
150C2×C4×C5—41no—
151C2×C4×C5—41no—
152C2×C4×C5—41no—
153C2×C4×C5C4×D412yes—
154C2×C4×C5#12011yescharacteristic
155C2×C4×C5#12112yes—
156C2×C4×C5#12311yescharacteristic
157C5×C8—44no—
158C5×C8—82no—
159C23×C4C5×D411yescharacteristic
160C2×M16—22no—
161#125—22no—
162#125—22no—
163#117—22no—
164#117—22no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4C2×C4×C511yescharacteristic
170C2×C4⋊C4C2×C4×C511yescharacteristic
171C2×C4⋊C4C2×C4×C511yescharacteristic
172C2×C4⋊C4C5×D411yescharacteristic
173C2×C22⋊C4—21no—
174C2×C22⋊C4—21no—
175C2×C22⋊C4C2×C4×C511yescharacteristic
176C2×C22⋊C4C5×D411yescharacteristic
177C2×C42—21no—
178C2×C42C5×D411yescharacteristic
179C2×C42C23×C511yescharacteristic
180C4⋊C8—24no—
181C4⋊C8—22no—
182C22⋊C8—24no—
183C22⋊C8—22no—
184#97—22no—
185#97C5×D414yes—
186C4×C8—22no—
187#95—21no—
188#95—21no—
189#95—21no—
190#95—21no—
191#95—21no—
192#95C2×C4×C511yescharacteristic
193#95C2×C4×C511yescharacteristic
194C22×C5—21no—
195C22×C5—21no—
196C22×C5—42no—
197C22×C5—41no—
198C22×C5—41no—
199C22×C5—41no—
200C22×C5—81no—
201C22×C5#38611yescharacteristic
202C22×C5#42111yescharacteristic
203C22×C5#42111yescharacteristic
204C4×C5—22no—
205C4×C5—21no—
206C4×C5—21no—
207C4×C5—22no—
208C4×C5—42no—
209C4×C5—41no—
210C4×C5—41no—
211C4×C5—41no—
212C4×C5—81no—
213C4×C5—81no—
214C4×C5—81no—
215C24C5×C22⋊C411yescharacteristic
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4C5×C22⋊C411yescharacteristic
225C22×C4C5×C22⋊C411yescharacteristic
226C22×C4C5×C22⋊C411yescharacteristic
227C22×C4C22×C4×C511yescharacteristic
228C22×C4C2×C5×D411yescharacteristic
229C22×C4C2×C5×D411yescharacteristic
230M16—42no—
231M16—42no—
232C2×C8—24no—
233C2×C8—42no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—22no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—41no—
241C4⋊C4—42no—
242C4⋊C4—41no—
243C22⋊C4—22no—
244C22⋊C4—22no—
245C22⋊C4—42no—
246C22⋊C4—42no—
247C42—21no—
248C42—21no—
249C42—42no—
250C42C2×C5×D412yes—
251C42C5×#4112yes—
252C2×C5—21no—
253C2×C5—21no—
254C2×C5—81no—
255C2×C5#188411yescharacteristic
256C2×C5#189711yescharacteristic
257C2×C5#191511yescharacteristic
258C23—21no—
259C23—21no—
260C23—21no—
261C23—41no—
262C23—41no—
263C23C2×C5×C22⋊C411yescharacteristic
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4C4×C5×D412yes—
290C2×C4C5×#12011yescharacteristic
291C2×C4C5×#12112yes—
292C2×C4C5×#12311yescharacteristic
293C8—44no—
294C8—82no—
295C5#939011yescharacteristic, direct product factor, Sylow
296C22—21no—
297C22—21no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22C5×#38611yescharacteristic
304C22C5×#42111yescharacteristic
305C22C5×#42111yescharacteristic
306C4—22no—
307C4—21no—
308C4—21no—
309C4—22no—
310C4—42no—
311C4—41no—
312C4—41no—
313C4—41no—
314C4—81no—
315C4—81no—
316C4—81no—
317C2—21no—
318C2—21no—
319C2—81no—
320C2C5×#188411yescharacteristic
321C2C5×#189711yescharacteristic
322C2C5×#191511yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×C42C23×C5
prime radicalC24×C5C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C5×#1528C2semidirect
5. C5×#1300C2semidirect
25. #9390C5direct (N × H)
63. #1528C2×C5semidirect
65. #1300C2×C5semidirect
295. C5#9390direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C5×#29212
C5×#26112
C5×#15282
C5×#14642
C5×#13002
#93905